problems met in stability calculations of offshore rigs...

International Ship Stability Workshop 2013

Proceedings of the 13th International Ship Stability Workshop, Brest 23-26 September

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Problems met in stability calculations of offshore rigs and how to deal

with them

Joost van Santen ([email protected])

GustoMSC, the Netherlands

ABSTRACT

For the calculation of the hydrostatic stability of mobile offshore units, various authorities have

nowadays adopted almost the same requirements. These requirements lean heavily on the

application of wind overturning moment, equilibrium angles, downflooding and range of stability.

A discussion of the various ways to calculate the righting arms is given together with problems met

in practice like backward sloping curves and heel angles for which the rig is unstable in trim or axis

direction. The use of the gain in potential energy is investigated as a means to arrive at realistic

righting arm curves. Though this suggests that free twist (or varying axis direction) is the preferred

method, it is not without problems of its own. At this moment there does not seem to be a robust

way to calculate stability other than using fixed trim (read: zero trim) and a fixed axis direction.

It is proposed to do (more) research into the actual reasons for a MODU to capsize due to

environmental loading, preferably by model testing with wind and waves.

KEYWORDS

semi submersible; jack up; hydrostatic stability; free trim; free twist

INTRODUCTION

In the assessment of the safety of a floating

offshore rig, hydrostatic stability plays a crucial

role. In the past decades, the requirements

focused on the stability parameters like initial

stability (GM) and ratio between area under the

righting- and wind overturning arm. Initially

these requirements were derived from the

requirements for ships. Additional insight

obtained from actual experience and

unfortunate accidents led to changes to the

requirements such that they became more

specific to the type of rig. Initially, each

classification society had its own set of rules.

In the past years, the criteria of the various

regulations attained a certain degree of

similarity though they still differ in details.

Quite often additional clarification is needed

regarding the proper interpretation of the

requirements.

Experience in the past years has shown that the

actual calculation of the righting arm curve is

not as straightforward as it looks. It seems that

the availability of powerful computer programs

has reduced the attention of the user to getting

reliable results. In the 1980’s a lot of

interesting research effort was put in

hydrostatic stability. For example, in the period

1975 to 1991 12 papers of the OTC conference

were devoted to this aspect, see figure 1

(Clauss, 1984, Collins et al, 1988, Dahle, 1985,

De Souza et al, 1978, Huang et al, 1982, Huse

et al, 1985, Kuo et al, 1977, Numata et al,

1975, Praught et al, 1985, Shark et al, 1989,

Soylemez et al, 1988, Stiansen et al, 1988).

Most of them did consider semi submersibles,

only one touched upon stability for jack-ups. In

this period, low frequency motions was a new

phenomenon which was hardly understood but

which caught great attention. After 1991,

interest in stability was lost (at least for the

OTC). At that time also two papers were

published which -at hindsight- hinted at the

problems to come (Vassalos, 1985 and van

Santen, 1986).



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Note that nowadays, a modern semi

submersible has much more reserve buoyancy

above the waterline than those of 1980’s.

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Number of OTC papers devoted to hydrostatic stability of semi submersibles

and jackups

semi submersibles (12)

jack-ups (1)

Fig. 1: OTC papers devoted to stability of MODU’s

Examples of offshore structures

Examples of typical offshore structures are

given in the figures below. Nowadays, a

modern semisubmersible is less transparent

than in the 1980’s and the deck provides a lot

of buoyancy (figure 2).

Fig. 2: Example of a large semi submersible.

Figure 3 gives an example of a large triangular

jack-up, characterized by legs length of about

200 m, and natural roll and pitch periods of

about 15 s.

At the lower end of the spectrum, small

installation jack-ups have recently emerged,

usually with four legs and a leg length about 80

m, see figure 4.

Fig. 3: Example of a large jack-up.

Fig. 4: Example of a small jack-up.

Summary review of requirements

Below, a schematic overview is given of the

requirements as found in the IMO-2009 rules.

It is certainly not meant to provide a detailed

overview of the requirements. For details,

reference is made to the specific requirements

of class, IACS and IMO.



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Operational condition

A distinction is made between transit,

operational and survival condition. For

survival, only intact has to be considered.

Intact, area requirement

The area under the righting arm curve should

be larger than the area under the wind heeling

curve by a given factor where a differentiation

is made between jack-ups and semi

submersibles. This assumes a sudden change of

the wind speed from 0 to a fixed value and that

induced heeling motion is undampened in still

water. The reason for the difference in the ratio

between semi submersibles and jack-ups is

unknown.

Damage

A distinction is made in waterline damage and

damage to a compartment somehow connected

to the sea. For waterline damage, the

penetration depth is limited to 1.5 m. For a

semi submersible the angle of heel after

damage (with wind) should not be greater than

a specific angle (17 degrees). In addition there

are some detailed requirements on the righting

arm in relation to the wind arm. Specific

requirements to the stability curve are given

when a compartment connected to the sea is

damaged.

For jack-ups, the rig should provide sufficient

buoyancy to withstand waterline damage.

When any compartment is damaged, a specific

requirement is set on the range of positive

stability, without the effect of wind and without

considering downflooding.

Watertightness

The rig should be watertight up to at least the

first intercept with the wind arm.

Weatertightness

The rig is to be weathertight up to the second

intercept with wind or at the angle where the

arm is zero again. Sometimes weathertightness

should be guaranteed up to the angle at which

the criteria are satisfied. This depends on

downflooding being accepted or not.

GM value

In earlier class rules, a requirement on

minimum GM was present, but not anymore.

Nowadays, a modern semi submersible is

allowed to operate with a GM of 0 m.

As is seen, the criteria focus on the following

aspects:

Sudden wind impact

First and second intercept

Downflooding

Water- and weather-tightness

Nowhere in the regulations, the influence of

waves is seen unless one views the escape of

“alternative stability criteria” as offered in

some rules as a means to include the effect of

waves.

The approach shows that the evaluation of

safety is done in a simplified and schematic

way. This has the advantage that it lends itself

for an analysis which should give equal result

independent of the calculation method. But,

there are two problems with this approach.

First, it is a very schematic representation of

how a rig capsizes. In nature, waves will be

present and the wind will not suddenly rise to

the maximum value. Second, doing the

calculation in a correct manner is not as simple

as it looks. Quite often, we have seen that

heeling axis directions are investigated which

have no link with reality. A particular problem

is that -as customary with ships- free trim is to

be used. In some cases, it can be shown that

when using free trim and selecting an

unfortunate axis direction, the rig is never

allowed to leave the quay.

On the other hand, the present rules do not give

much room for improvement. To improve the

situation one has to go back to the basics and

develop a better understanding of the capsize

mechanism.



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Experience with a variety of structures shows

that even a seemingly simple stability

calculation is not as straightforward as it looks.

Note that the maximum loading condition of

the rig and thus its commercial value depends

on it. Therefore, it is stressed that unrealistic

results of stability calculations must be

avoided.

Stability calculations

There are various ways to perform a stability

analysis. The most simple and failsafe

approach is where the axis is fixed and rig is

heeled around this axis with zero trim. Various

axis directions are to be investigated to arrive

at the most critical one.

Similar as with ships, free trim was introduced

as a means to obtain the lowest righting arm

curve. For a given axis direction and heel

angle, free trim results in the lowest potential

energy contained in the rig. The reason being

that by setting the rig free to trim, potential

energy is released which would otherwise be

present due to forcing the rig to have a non-

zero trim moment. But this is only true when

the rig is stable in trim.

X

Z

Free trim

Heel

Heel angle

Fig. 5: Definition of heel and trim.

Within GustoMSC, the free twist method (also

called variable axis direction) has been

developed (Santen, 1986 and Santen, 2009). In

this method, the direction of the heeling axis is

varied such that the moment around the initial

vertical axis is zero. By doing this, the

trimming moment (being the horizontal

component of the moment around the inclined

twist axis) is zero whilst the trim angle is nil. In

general, it results in the lowest energy build up

in the system (van Santen STAB 2009).

Fig. 6: Definition of twist and heel

Note that in the free trim method the waterline

on an initially horizontal deck does not remain

parallel with the heeling axis, see also figure 5.

In contrast, for free twist, the waterline on an

initially horizontal deck is always parallel with

the heeling axis, see figure 6.

For ship-like structures, the free trim method is

a sensible way to do the calculation. But, in

this case the axis direction is always fixed to be

the longitudinal axis. Would we perform the

stability calculation for other axis directions,

strange things occur. For instance, if we select

a near transverse axis direction, the ship would

experience large trim angles in order to get

zero trim moment. As an example, consider a

barge shown in figure 6. Figure 7 shows two

righting arms for a longitudinal and almost

transverse axis direction, whilst figure 8 shows

the trim angles. For an axis direction of 80

degrees, large trim angles are observed.

By van Santen (STAB2009 and JU2009) more

details are given for this case. Interestingly, for

a ship, everyone will reject the righting arm

obtained for a near transverse axis, but for

offshore rigs it is not.



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Fig. 7: Righting arms for free trim calculations for a

longitudinal and almost transverse axis direction

Fig. 8: Trim angles for free trim calculations for a longitudinal

and almost transverse axis direction

Would we use free twist, the heeling axis

direction remains almost longitudinal.

When using free twist, the energy in the system

is minimized whilst heeling. The theoretical

proof is given by Santen (STAB2009). For the

barge, the free twist path is shown in figure 9.

Fig. 9: Path of minimum energy build up for the barge

In this case, using free twist results in a

realistic righting arm.

Large jack-up

For a triangular jack-up the preferred axis

direction is not obvious and often an axis

direction is selected for which large trim angles

will be observed. An example is given for a

large jack-up in intact condition which had to

satisfy the NMD requirement of 30 degree

range up to the second intercept with the wind

arm. For an axis direction of 90 degrees the

bow is pressed into the water. At around 25

degrees heel, a discontinuity in the curve is

observed, see figure 10.

Would we force the heel to increase (which is

the customary way to do the calculation) a

jump in the trim angle will be observed, see

figure 11. The proper continuation by the

0

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4

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0 10 20 30 40

Rig

htin

g ar

m (m

)

Heel angle (deg)

Free trim calculationsFree trim increasing heel

Free trim, combined heel and trim vector varies

Discontinuity

UnstableUnstable

Fig. 10: Free trim calculations for a large jack-up, righting arm

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-10

-5

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5

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20

25

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0 10 20 30 40

Trim

an

gle

(de

g)

Heel angle (deg)

Free trim increasing heel

Free trim, combined heel and trim vector varies

Discontinuity in trim

Fig. 11: Free trim calculations for a large jack-up, trim angle



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backward sloping curve shows a gradual

increase in the trim angle whilst the heel angle

is to be reduced.

Most computer code can’t calculate such a

backward going curve. In a conventional

calculation, the heel angle would be forced to

increase beyond 25 degrees, which would

result in a righting arm belonging to a

completely different position which is not a

proper continuation of the curve. This can be

checked by looking and the rate of change in

potential energy which should be equal to the

energy input. Interestingly, even with zero

VCG, the 30 degree NMD range can’t be

reached for an axis direction of 90 degrees.

Would we use an axis direction of 270 degrees,

the trim angle would be small and the 30

degree range would indeed be satisfied. This is

shown in the energy plot, figure 12, for a draft

5.5 m where the VCB reaches a maximum

(corresponding with the second zero crossing

of the righting arm) for a heel angle of about 32

degrees.

Fig. 12: Energy build up for a large jack-up

Small jack-up

Small wind turbine installation jack-ups are

classed as jack-ups but their length over width

ration is much larger than for the large drilling

jack-ups. For operational reasons large centre

compartments are present. When such a

compartment is damaged the range of positive

stability has to be larger than a specific value

being 7+1.5*static angle. For the hull shown in

Figure 13, model of a damaged jack-up

0

0.5

1

1.5

2

2.5

0 5 10 15 20 25 30

Rig

hti

ng

arm

(m)

Heel angle (deg)

Righting arm

Free trim, stable

Free trim, unstable

Free twist, stable

Fig. 14: Righting arms for small damaged jack-up

figure 13 with a damaged forward centre

compartment, a free trim calculation results in

a range of stability of about 19 degrees, see

figure 14. A problem with the results is that for

a heel angle exceeding 11 degrees, the vessel

becomes unstable in trim. So, though the

calculation indicates a range of positive

stability of 19 degrees this would not be

confirmed by actual testing as the vessel would

capsize when heeled beyond about 11 degrees.

The result of a free twist calculation shows a

much smaller range of positive stability of

about 13 degrees. For a proper interpretation it

is necessary that in addition to the righting arm,

the results must indicate if the vessel is stable

in trim (or twist). Would we perform the

stability calculation with a fixed trim (of 0 deg)

the resulting righting arms do not cover either

MSC Stability program(DAMAST-W32), version:V 6.61 run on 03-Jun-2013 11:33:35 by:joost.vansanten

M:\Sources\damast\Publications javs\ISSW2013\11368 ng2500\3.75 m draft\01_DAMAST\STABILITY MODEL NG2500-REVC.inp (DOS)

non protected openings

weathertight openings

X Y

Z



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the free trim or free twist calculation, not even

a reasonable manner, see figure 15.

Fig. 15: Righting arms for various calculation methods

The reason for this is also seen in the energy

plot for small heel angles. There is a sudden

change when heeled from the equilibrium

position (around 4.1 degrees heel) to larger

heel angles.

Fig. 16: Energy plot for the damaged jack-up at small heel

angles

Semi submersible

Whilst the above suggest that free twist is the

preferred method to calculate the righting arm,

it is not free of problems of its own. For a semi

submersible it is not uncommon that in a free

twist approach, the righting arm curve has

Fig. 17: Righting arm for a semi submersible, using free twist

Fig. 18: Axis direction using free twist

Fig. 19: VCB plot

unstable parts, see figure 17. When during

progressive heel an unstable position is

reached, the rig will suddenly change axis

direction such that a new stable position is

attained. This effect is visualized in figure 18

which shows the heeling axis direction for a

free twist type of calculation and in figure 19



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which shows the energy plot. In the energy

plot, the path will follow the peaks and troughs,

but only the troughs, being local minima,

indicate stable positions. Note that when

increasing the heel angle, the axis direction will

suddenly change at a heel angle of about 26

degrees whilst for a decreasing heel angle it

will suddenly change back at a heel angle about

19 degrees.

Modern semi submersible have a large amount

of buoyancy above the waterline which makes

it difficult to capsize them in intact conditions,

even considering large waves. This is in

contrast with jack-ups where the wave action is

a factor to consider when looking at intact

stability, (Standing et al 1999, van Santen

1999). Casualties with semi submersible are

highly related to the rig not being intact

anymore and thus susceptible to downflooding.

Conclusions

1. At this time, using stability parameters

as a measure of safety ofoffshore rigs

seems to be the only viable method.

Though, especially for jack-ups, wave

action can be important, there are no

proven and generally accepted methods

for dealing with wave action yet.

2. Allowing the rig to trim or twist freely

is sensible as this generally leads to the

slowest build up of potential energy for

increasing heel angles. Thus the lowest

righting arm curve is achieved.

3. Extending the free trim approach as

used for ships to offshore units, in

combination with a varying heeling axis

direction, may lead to severe

interpretation problems. Awareness of

these problems is not widespread

amongst the industry and requires more

attention.

4. Observing large trim angles during the

stability calculation indicates that the

selected heeling axis is not proper.

5. Apart from choosing the proper axis

direction, one must also take care that

rig is stable in trim or twist up to the

maximum heel angle needed for the

evaluation of a particular criterion.

Preferably the rig should be stable in

trim or twist up to the point of capsize

in heel.

6. The stability calculation procedure as

now briefly given by class and

authorities as “free trim” and “most

critical” should be accompanied by a

clarification note explaining how to do

the calculation and how to handle the

various problems met.

Recommendations

In the formal education of naval architecture

more attention should be paid to the stability

calculation of offshore rigs. It is essential that

the students have a good understanding of the

underlying principles. Also, it is important that

results of computer programs should not be

accepted without a good insight in the

calculation method and in the validity of the

results. In order to offer this insight, programs

should output information like trim angle, axis

direction (if variable), VCB value, stability of

the position and identify possible

discontinuities in the curve. It is the authors’

opinion that many programs fail in this respect.

Though in the 1980’s studies have been done

into the possible capsize and downflooding of a

semi submersible, there still is a need to

improve actual knowledge of the capsize

mechanism in a real world environment. This is

especially true when considering stability of

jack-ups.

Disclaimer

The opinions expressed are those of the author

and not those of the company or organization

that he is representing.

REFERENCES

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Accidental Damage, OTC 4729, 1984

Collins,JI, and Grove,TW, Model Tests Of A Generic

Semisubmersible Related To A Study Assessing Stability

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9

Criteria , OTC 5801, 1988

Dahle,LA, Mobile Platform Stability: Project Synthesis With

Recommendations for New Philosophies for Stability

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De Souza, PMF and Miller, NS, The Intact and damaged

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1982

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